In this paper a new approach to state estimation in distribution networks is proposed. This approach is more robust against large uncertainties of the state estimation inputs than the conventional method. Traditionally, the goal of state estimation was to estimate the exact value of network parameters, such as voltages and currents. This works well in transmission networks where many real time measurements are available. In distribution networks, however, only few real-time measurements are available. This means that the estimated state can be significantly different from the actual network state. Therefore, the focus of the proposed robust state estimation is shifted from estimating the exact values of the network parameters to the confidence that these parameters are within their respective constraints. This approach is able to provide useful results for distribution network operation, even if large uncertainties are present in the estimated network state.